library(vegan)## Loading required package: permute## Loading required package: lattice## This is vegan 2.5-6library(lattice)
data(BCI)
?BCI
## UTM Coordinates (in metres)
BCI_xy = data.frame(x = rep(seq(625754, 626654, by=100), each=5),
y = rep(seq(1011569, 1011969, by=100), len=50))
plot(BCI_xy)
Overall Data (just wanted to see)
sr = apply(BCI, 1, function(x) sum(x > 0))
hist(sr)
plot(BCI_xy, cex = sr/max(sr))
col_brks = hist(sr, plot=F)$breaks
col_indices = as.numeric(cut(sr, col_brks))
cols = rev(terrain.colors(length(col_brks)))
plot(BCI_xy, cex=2, pch=19, col=cols[col_indices])
# calculate Euclidean distance between richness and spatial coordinates
sr_dist = dist(sr)
xy_dist = dist(BCI_xy)max_dist = max(xy_dist) / 2
# plot result
plot(xy_dist, sr_dist)
abline(lm(sr_dist ~ xy_dist), lwd=3, col='red')
lines(lowess(xy_dist, sr_dist), lwd=3, col='pink')
abline(v = max_dist, col='red', lwd=3, lty=2)
# compute correlation
obs_cor = cor(xy_dist, sr_dist)
obs_cor## [1] 0.004339913# carry out a permutation test for significance:
nperm = 1000
null_cor = obs_cor
for (i in 2:nperm) {
# shuffle the rows of the spatial coordinates
tmp_xy = BCI_xy[sample(nrow(BCI_xy)), ]
# correlation between the shuffled spatial coordinates and sr_dist
null_cor[i] = cor(dist(tmp_xy), sr_dist)
}
# compute the p-value
sum(null_cor >= obs_cor) / nperm ## [1] 0.48# carry out the same analysis
sr_mantel = mantel(xy_dist, sr_dist)
sr_mantel##
## Mantel statistic based on Pearson's product-moment correlation
##
## Call:
## mantel(xdis = xy_dist, ydis = sr_dist)
##
## Mantel statistic r: 0.00434
## Significance: 0.434
##
## Upper quantiles of permutations (null model):
## 90% 95% 97.5% 99%
## 0.0678 0.0883 0.1087 0.1290
## Permutation: free
## Number of permutations: 999- Common
alseis = BCI[,"Alseis.blackiana"]
alseis## [1] 25 26 18 23 16 14 18 14 16 14 14 19 8 17 15 25 31 7 13 10 12 22 5 14 20
## [26] 7 17 16 15 36 11 21 24 42 93 8 19 25 38 65 13 13 8 13 10 29 17 12 6 9plot(BCI_xy, cex = alseis/max(alseis))
##ggplot solution
library(ggplot2)
ggplot(BCI_xy, aes(x=x, y=y, size=alseis)) + geom_point() + scale_size_continuous(range = c(1,5))
col_brks = hist(alseis, plot=F)$breaks
col_indices = as.numeric(cut(alseis, col_brks))
cols = rev(terrain.colors(length(col_brks)))
plot(BCI_xy, cex=2, pch=19, col=cols[col_indices])
# calculate Euclidean distance between abundance and spatial coordinates
ab_dist = dist(alseis)
xy_dist = dist(BCI_xy)
max_dist = max(xy_dist) / 2plot(xy_dist, ab_dist)
abline(lm(ab_dist ~ xy_dist), lwd=3, col='red')
lines(lowess(xy_dist, ab_dist), lwd=3, col='pink')
abline(v = max_dist, col='red', lwd=3, lty=2)
# compute correlation
obs_cor = cor(xy_dist, ab_dist)
obs_cor## [1] -0.02348007# carry out a permutation test for significance:
nperm = 1000
null_cor = obs_cor
for (i in 2:nperm) {
# shuffle the rows of the spatial coordinates
tmp_xy = BCI_xy[sample(nrow(BCI_xy)), ]
# correlation between the shuffled spatial coordinates and ab_dist
null_cor[i] = cor(dist(tmp_xy), ab_dist)
}
# compute the p-value
sum(null_cor >= obs_cor) / nperm ## [1] 0.593ab_mantel = mantel(xy_dist, ab_dist)
ab_mantel##
## Mantel statistic based on Pearson's product-moment correlation
##
## Call:
## mantel(xdis = xy_dist, ydis = ab_dist)
##
## Mantel statistic r: -0.02348
## Significance: 0.603
##
## Upper quantiles of permutations (null model):
## 90% 95% 97.5% 99%
## 0.0818 0.1057 0.1210 0.1390
## Permutation: free
## Number of permutations: 999##examine community
## compute bray curtis distance for the community matrix
comm_dist = vegdist(BCI)
plot(xy_dist, comm_dist)
abline(lm(comm_dist ~ xy_dist), lwd=3, col='red')
lines(lowess(xy_dist, comm_dist), lwd=3, col='pink')
lines(lowess(xy_dist, comm_dist, f=0.1), lwd=3, col='blue')
abline(v = max_dist, col='red', lwd=3, lty=2)
comm_mantel = mantel(xy_dist, comm_dist)
comm_mantel##
## Mantel statistic based on Pearson's product-moment correlation
##
## Call:
## mantel(xdis = xy_dist, ydis = comm_dist)
##
## Mantel statistic r: 0.4078
## Significance: 0.001
##
## Upper quantiles of permutations (null model):
## 90% 95% 97.5% 99%
## 0.0642 0.0878 0.1019 0.1130
## Permutation: free
## Number of permutations: 999ab_corlog = mantel.correlog(ab_dist, xy_dist)
comm_corlog = mantel.correlog(comm_dist, xy_dist)
ab_corlog##
## Mantel Correlogram Analysis
##
## Call:
##
## mantel.correlog(D.eco = ab_dist, D.geo = xy_dist)
##
## class.index n.dist Mantel.cor Pr(Mantel) Pr(corrected)
## D.cl.1 136.870241 144.000000 0.026911 0.105 0.105
## D.cl.2 210.610723 376.000000 -0.015646 0.282 0.282
## D.cl.3 284.351204 390.000000 -0.046374 0.028 0.084 .
## D.cl.4 358.091686 148.000000 -0.015208 0.230 0.460
## D.cl.5 431.832168 372.000000 -0.044131 0.074 0.296
## D.cl.6 505.572649 266.000000 -0.011319 0.179 0.537
## D.cl.7 579.313131 168.000000 NA NA NA
## D.cl.8 653.053613 100.000000 NA NA NA
## D.cl.9 726.794094 154.000000 NA NA NA
## D.cl.10 800.534576 88.000000 NA NA NA
## D.cl.11 874.275058 50.000000 NA NA NA
## D.cl.12 948.015539 24.000000 NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1comm_corlog##
## Mantel Correlogram Analysis
##
## Call:
##
## mantel.correlog(D.eco = comm_dist, D.geo = xy_dist)
##
## class.index n.dist Mantel.cor Pr(Mantel) Pr(corrected)
## D.cl.1 136.870241 144.000000 0.181547 0.001 0.001 ***
## D.cl.2 210.610723 376.000000 0.133245 0.001 0.002 **
## D.cl.3 284.351204 390.000000 -0.017807 0.253 0.253
## D.cl.4 358.091686 148.000000 -0.029965 0.091 0.182
## D.cl.5 431.832168 372.000000 -0.055778 0.039 0.117
## D.cl.6 505.572649 266.000000 -0.087321 0.001 0.006 **
## D.cl.7 579.313131 168.000000 NA NA NA
## D.cl.8 653.053613 100.000000 NA NA NA
## D.cl.9 726.794094 154.000000 NA NA NA
## D.cl.10 800.534576 88.000000 NA NA NA
## D.cl.11 874.275058 50.000000 NA NA NA
## D.cl.12 948.015539 24.000000 NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##no significance in the abundance of Alseis but there is significant in the community structure (non linear)par(mfrow=c(1,2))
plot(ab_corlog)
mtext(side=3, 'Species Abundance')
abline(v = max_dist, col='red', lwd=3, lty=2)
plot(comm_corlog)
mtext(side=3, 'Community Composition')
abline(v = max_dist, col='red', lwd=3, lty=2)
Rare
andira = BCI[,"Andira.inermis"]
andira## [1] 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 2 0 0 1 1 2 0 2 0 1 1 2 0 0 2 1 0 0 0 0
## [39] 0 0 1 1 2 0 0 0 0 1 2 1plot(BCI_xy, cex = andira/max(andira))
##ggplot
ggplot(BCI_xy, aes(x=x, y=y, size=andira)) + geom_point() + scale_size_continuous(range = c(1,5))
col_brks = hist(andira, plot=F)$breaks
col_indices = as.numeric(cut(andira, col_brks))
cols = rev(terrain.colors(length(col_brks)))
plot(BCI_xy, cex=2, pch=19, col=cols[col_indices])
andira_dist = dist(andira)
xy_dist = dist(BCI_xy)
max_dist = max(xy_dist) / 2plot(xy_dist, andira_dist)
abline(lm(andira_dist ~ xy_dist), lwd=3, col='red')
lines(lowess(xy_dist, andira_dist), lwd=3, col='pink')
abline(v = max_dist, col='red', lwd=3, lty=2)
andira_mantel = mantel(xy_dist, andira_dist)
andira_mantel##
## Mantel statistic based on Pearson's product-moment correlation
##
## Call:
## mantel(xdis = xy_dist, ydis = andira_dist)
##
## Mantel statistic r: -0.05389
## Significance: 0.889
##
## Upper quantiles of permutations (null model):
## 90% 95% 97.5% 99%
## 0.0640 0.0845 0.0982 0.1199
## Permutation: free
## Number of permutations: 999andira_corlog = mantel.correlog(andira_dist, xy_dist)
andira_corlog##
## Mantel Correlogram Analysis
##
## Call:
##
## mantel.correlog(D.eco = andira_dist, D.geo = xy_dist)
##
## class.index n.dist Mantel.cor Pr(Mantel) Pr(corrected)
## D.cl.1 136.8702408 144.0000000 -0.0216764 0.233 0.233
## D.cl.2 210.6107225 376.0000000 -0.0324079 0.138 0.276
## D.cl.3 284.3512042 390.0000000 -0.0251373 0.201 0.414
## D.cl.4 358.0916859 148.0000000 -0.0143570 0.314 0.603
## D.cl.5 431.8321676 372.0000000 -0.0026076 0.486 0.804
## D.cl.6 505.5726492 266.0000000 0.0029042 0.499 1.000
## D.cl.7 579.3131309 168.0000000 NA NA NA
## D.cl.8 653.0536126 100.0000000 NA NA NA
## D.cl.9 726.7940943 154.0000000 NA NA NA
## D.cl.10 800.5345760 88.0000000 NA NA NA
## D.cl.11 874.2750577 50.0000000 NA NA NA
## D.cl.12 948.0155393 24.0000000 NA NA NApar(mfrow=c(1,2))
plot(andira_corlog)
mtext(side=3, 'Species Abundance')
abline(v = max_dist, col='red', lwd=3, lty=2)
There is no evidence of spatial dependance in both the common (Alseis) and rare (Andira) species.
2.one species
sp_ids = c("Cordia.lasiocalyx", "Hirtella.triandra",
"Picramnia.latifolia", "Quassia.amara",
"Tabernaemontana.arborea", "Trattinnickia.aspera",
"Xylopia.macrantha")
BCI_ids = cbind("Drypetes.standleyi", "Cordia.lasiocalyx", "Hirtella.triandra",
"Picramnia.latifolia", "Quassia.amara",
"Tabernaemontana.arborea", "Trattinnickia.aspera",
"Xylopia.macrantha")sp_a <- apply(BCI_ids, 1, function(x) sum(x > 0))
sp_data = data.frame(sp_a, BCI, BCI_xy)
BCI_sub = subset(sp_data, select = BCI_ids)library(nlme)
sp_lm = gls(Drypetes.standleyi ~ Hirtella.triandra, data=BCI_sub)
var_sp = Variogram(sp_lm, form= ~ BCI_xy$x + BCI_xy$y)
plot(var_sp)
res = residuals(sp_lm)
plot(dist(sp_data[, c('x', 'y')]), dist(res))
lines(lowess(dist(sp_data[, c('x', 'y')]), dist(res)), col='red', lwd=2)
abline(v = max_dist, col='red', lwd=3, lty=2)
x = BCI_xy$x
y = BCI_xy$y
sp_exp = update(sp_lm, corr=corExp(form=~x + y))
plot(Variogram(sp_exp, maxDist = max_dist))
plot(Variogram(sp_exp, resType='normalized', maxDist = max_dist))
sp_exp_nug = update(sp_exp, corr=corExp(form = ~x +y , nugget=T))
plot(Variogram(sp_exp_nug, maxDist = max_dist))
sp_rat_nug = update(sp_lm, corr=corRatio(form = ~x + y, nugget=T))
plot(Variogram(sp_rat_nug, maxDist = max_dist))
plot(Variogram(sp_rat_nug, resType='n', maxDist = max_dist))
col_brks = hist(residuals(sp_rat_nug), plot=F)$breaks
col_indices = as.numeric(cut(residuals(sp_rat_nug), col_brks))
cols = rev(terrain.colors(length(col_brks)))
plot(BCI_xy, cex=2, pch=19, col=cols[col_indices])
anova(sp_lm, sp_exp, sp_exp_nug, sp_rat_nug, test=F)## Model df AIC BIC logLik
## sp_lm 1 3 346.1696 351.7832 -170.0848
## sp_exp 2 4 312.5365 320.0213 -152.2682
## sp_exp_nug 3 5 313.2119 322.5679 -151.6059
## sp_rat_nug 4 5 310.6244 319.9804 -150.3122summary(sp_lm)## Generalized least squares fit by REML
## Model: Drypetes.standleyi ~ Hirtella.triandra
## Data: BCI_sub
## AIC BIC logLik
## 346.1696 351.7832 -170.0848
##
## Coefficients:
## Value Std.Error t-value p-value
## (Intercept) 0.6267619 1.7550545 0.357118 0.7226
## Hirtella.triandra 0.3724844 0.1038112 3.588094 0.0008
##
## Correlation:
## (Intr)
## Hirtella.triandra -0.806
##
## Standardized residuals:
## Min Q1 Med Q3 Max
## -1.5837021 -0.5405355 -0.2411211 0.1461580 4.0034096
##
## Residual standard error: 7.352136
## Degrees of freedom: 50 total; 48 residualsummary(sp_exp)## Generalized least squares fit by REML
## Model: Drypetes.standleyi ~ Hirtella.triandra
## Data: BCI_sub
## AIC BIC logLik
## 312.5365 320.0213 -152.2682
##
## Correlation Structure: Exponential spatial correlation
## Formula: ~x + y
## Parameter estimate(s):
## range
## 1.399944e+13
##
## Coefficients:
## Value Std.Error t-value p-value
## (Intercept) 14.473746 1746021.3 0.000008290 1.000
## Hirtella.triandra -0.000646 0.1 -0.006275689 0.995
##
## Correlation:
## (Intr)
## Hirtella.triandra 0
##
## Standardized residuals:
## Min Q1 Med Q3 Max
## -8.288079e-06 -8.284289e-06 -7.138550e-06 -3.843500e-06 1.405581e-05
##
## Residual standard error: 1746021
## Degrees of freedom: 50 total; 48 residualsummary(sp_exp_nug)## Generalized least squares fit by REML
## Model: Drypetes.standleyi ~ Hirtella.triandra
## Data: BCI_sub
## AIC BIC logLik
## 313.2119 322.5679 -151.6059
##
## Correlation Structure: Exponential spatial correlation
## Formula: ~x + y
## Parameter estimate(s):
## range nugget
## 3.029648e+08 1.815151e-07
##
## Coefficients:
## Value Std.Error t-value p-value
## (Intercept) 12.254798 6300.289 0.00194512 0.9985
## Hirtella.triandra 0.017615 0.099 0.17747775 0.8599
##
## Correlation:
## (Intr)
## Hirtella.triandra 0
##
## Standardized residuals:
## Min Q1 Med Q3 Max
## -0.0019870533 -0.0019562986 -0.0016402511 -0.0007709315 0.0041779703
##
## Residual standard error: 6300.295
## Degrees of freedom: 50 total; 48 residualsummary(sp_rat_nug)## Generalized least squares fit by REML
## Model: Drypetes.standleyi ~ Hirtella.triandra
## Data: BCI_sub
## AIC BIC logLik
## 310.6244 319.9804 -150.3122
##
## Correlation Structure: Rational quadratic spatial correlation
## Formula: ~x + y
## Parameter estimate(s):
## range nugget
## 752.28335795 0.04166127
##
## Coefficients:
## Value Std.Error t-value p-value
## (Intercept) 14.088134 14.874137 0.9471564 0.3483
## Hirtella.triandra 0.011441 0.087993 0.1300210 0.8971
##
## Correlation:
## (Intr)
## Hirtella.triandra -0.167
##
## Standardized residuals:
## Min Q1 Med Q3 Max
## -0.7428201 -0.7362643 -0.6323781 -0.3420863 1.2834076
##
## Residual standard error: 19.19677
## Degrees of freedom: 50 total; 48 residualRational model with the nugget fit better then without spatial error terms
all species
sp_all_lm = gls(Drypetes.standleyi ~ Cordia.lasiocalyx + Hirtella.triandra + Picramnia.latifolia + Quassia.amara + Tabernaemontana.arborea + Trattinnickia.aspera + Xylopia.macrantha , data=sp_data)
plot(Variogram(sp_all_lm, form= ~ BCI_xy$x + BCI_xy$y))
res = residuals(sp_all_lm)
plot(dist(sp_data[, c('x', 'y')]), dist(res))
lines(lowess(dist(sp_data[, c('x', 'y')]), dist(res)), col='red', lwd=2)
abline(v = max_dist, col='red', lwd=3, lty=2)
sp_all_exp = update(sp_all_lm, corr=corExp(form=~x + y))
plot(Variogram(sp_all_exp, maxDist = max_dist))
plot(Variogram(sp_all_exp, resType='normalized', maxDist = max_dist))
sp_all_exp_nug = update(sp_all_exp, corr=corExp(form=~x + y, nugget=T))
plot(Variogram(sp_all_exp_nug, maxDist = max_dist))
sp_all_rat_nug = update(sp_all_lm, corr=corRatio(form=~x + y, nugget=T))
plot(Variogram(sp_all_rat_nug, maxDist = max_dist))
plot(Variogram(sp_all_rat_nug, resType='n', maxDist = max_dist))
col_brks = hist(residuals(sp_all_rat_nug), plot=F)$breaks
col_indices = as.numeric(cut(residuals(sp_all_rat_nug), col_brks))
cols = rev(terrain.colors(length(col_brks)))
plot(BCI_xy, cex=2, pch=19, col=cols[col_indices])
col_brks = hist(residuals(sp_all_exp_nug), plot=F)$breaks
col_indices = as.numeric(cut(residuals(sp_all_exp_nug), col_brks))
cols = rev(terrain.colors(length(col_brks)))
plot(BCI_xy, cex=2, pch=19, col=cols[col_indices])
anova(sp_all_lm, sp_all_exp, sp_all_exp_nug, sp_all_rat_nug, test=F)## Model df AIC BIC logLik
## sp_all_lm 1 9 307.1163 322.7554 -144.5582
## sp_all_exp 2 10 301.6062 318.9829 -140.8031
## sp_all_exp_nug 3 11 301.9592 321.0735 -139.9796
## sp_all_rat_nug 4 11 303.1486 322.2630 -140.5743summary(sp_all_lm)## Generalized least squares fit by REML
## Model: Drypetes.standleyi ~ Cordia.lasiocalyx + Hirtella.triandra + Picramnia.latifolia + Quassia.amara + Tabernaemontana.arborea + Trattinnickia.aspera + Xylopia.macrantha
## Data: sp_data
## AIC BIC logLik
## 307.1163 322.7554 -144.5582
##
## Coefficients:
## Value Std.Error t-value p-value
## (Intercept) -1.051752 2.1175346 -0.496687 0.6220
## Cordia.lasiocalyx 0.428920 0.2039316 2.103255 0.0415
## Hirtella.triandra 0.122279 0.0802638 1.523462 0.1351
## Picramnia.latifolia 0.662259 0.6358905 1.041468 0.3036
## Quassia.amara 4.085661 2.2842770 1.788602 0.0809
## Tabernaemontana.arborea -0.249725 0.1491192 -1.674667 0.1014
## Trattinnickia.aspera 1.349323 0.7147412 1.887848 0.0660
## Xylopia.macrantha 0.548832 0.1468772 3.736672 0.0006
##
## Correlation:
## (Intr) Crd.ls Hrtll. Pcrmn. Qss.mr Tbrnm. Trttn.
## Cordia.lasiocalyx -0.618
## Hirtella.triandra -0.212 -0.354
## Picramnia.latifolia 0.025 -0.019 -0.381
## Quassia.amara 0.163 -0.378 0.307 -0.302
## Tabernaemontana.arborea -0.708 0.245 0.163 -0.113 0.148
## Trattinnickia.aspera -0.139 0.187 -0.311 0.308 -0.708 -0.144
## Xylopia.macrantha -0.140 -0.125 0.156 -0.463 0.314 0.279 -0.294
##
## Standardized residuals:
## Min Q1 Med Q3 Max
## -1.87708765 -0.42701500 -0.04032793 0.23615609 3.38768871
##
## Residual standard error: 4.539713
## Degrees of freedom: 50 total; 42 residualsummary(sp_all_exp)## Generalized least squares fit by REML
## Model: Drypetes.standleyi ~ Cordia.lasiocalyx + Hirtella.triandra + Picramnia.latifolia + Quassia.amara + Tabernaemontana.arborea + Trattinnickia.aspera + Xylopia.macrantha
## Data: sp_data
## AIC BIC logLik
## 301.6062 318.9829 -140.8031
##
## Correlation Structure: Exponential spatial correlation
## Formula: ~x + y
## Parameter estimate(s):
## range
## 480.0567
##
## Coefficients:
## Value Std.Error t-value p-value
## (Intercept) 2.3485197 6.154919 0.381568 0.7047
## Cordia.lasiocalyx 0.1208390 0.179811 0.672033 0.5052
## Hirtella.triandra 0.0191759 0.098501 0.194677 0.8466
## Picramnia.latifolia 0.2014516 0.509196 0.395627 0.6944
## Quassia.amara 1.2792289 1.847570 0.692385 0.4925
## Tabernaemontana.arborea 0.0674943 0.133782 0.504511 0.6165
## Trattinnickia.aspera 1.8115374 0.525147 3.449582 0.0013
## Xylopia.macrantha 0.3388574 0.156874 2.160064 0.0365
##
## Correlation:
## (Intr) Crd.ls Hrtll. Pcrmn. Qss.mr Tbrnm. Trttn.
## Cordia.lasiocalyx -0.226
## Hirtella.triandra -0.309 -0.022
## Picramnia.latifolia 0.045 -0.066 -0.369
## Quassia.amara -0.059 -0.304 0.321 -0.142
## Tabernaemontana.arborea -0.240 -0.016 0.288 -0.221 0.112
## Trattinnickia.aspera -0.069 0.168 -0.237 0.212 -0.633 -0.041
## Xylopia.macrantha -0.056 -0.137 -0.063 0.109 0.290 0.102 -0.186
##
## Standardized residuals:
## Min Q1 Med Q3 Max
## -1.0051632 -0.5235683 -0.3176178 0.2208753 2.3746027
##
## Residual standard error: 8.628464
## Degrees of freedom: 50 total; 42 residualsummary(sp_all_exp_nug)## Generalized least squares fit by REML
## Model: Drypetes.standleyi ~ Cordia.lasiocalyx + Hirtella.triandra + Picramnia.latifolia + Quassia.amara + Tabernaemontana.arborea + Trattinnickia.aspera + Xylopia.macrantha
## Data: sp_data
## AIC BIC logLik
## 301.9592 321.0735 -139.9796
##
## Correlation Structure: Exponential spatial correlation
## Formula: ~x + y
## Parameter estimate(s):
## range nugget
## 5.424635e+07 2.451077e-06
##
## Coefficients:
## Value Std.Error t-value p-value
## (Intercept) 3.0501045 1785.0597 0.001709 0.9986
## Cordia.lasiocalyx 0.1426666 0.1895 0.752752 0.4558
## Hirtella.triandra -0.0017714 0.0904 -0.019600 0.9845
## Picramnia.latifolia 0.2863335 0.5274 0.542880 0.5901
## Quassia.amara 1.3263643 1.9368 0.684818 0.4972
## Tabernaemontana.arborea 0.0407530 0.1395 0.292085 0.7717
## Trattinnickia.aspera 1.8170749 0.5730 3.171303 0.0028
## Xylopia.macrantha 0.4086700 0.1537 2.659324 0.0110
##
## Correlation:
## (Intr) Crd.ls Hrtll. Pcrmn. Qss.mr Tbrnm. Trttn.
## Cordia.lasiocalyx -0.001
## Hirtella.triandra -0.001 -0.098
## Picramnia.latifolia 0.000 0.017 -0.360
## Quassia.amara 0.000 -0.292 0.344 -0.193
## Tabernaemontana.arborea -0.001 -0.020 0.160 -0.197 0.088
## Trattinnickia.aspera 0.000 0.165 -0.276 0.255 -0.655 -0.036
## Xylopia.macrantha 0.000 -0.066 -0.037 -0.048 0.306 0.140 -0.183
##
## Standardized residuals:
## Min Q1 Med Q3 Max
## -0.0049325435 -0.0029088009 -0.0020671675 0.0005570041 0.0103697005
##
## Residual standard error: 1785.068
## Degrees of freedom: 50 total; 42 residualsummary(sp_all_rat_nug)## Generalized least squares fit by REML
## Model: Drypetes.standleyi ~ Cordia.lasiocalyx + Hirtella.triandra + Picramnia.latifolia + Quassia.amara + Tabernaemontana.arborea + Trattinnickia.aspera + Xylopia.macrantha
## Data: sp_data
## AIC BIC logLik
## 303.1486 322.263 -140.5743
##
## Correlation Structure: Rational quadratic spatial correlation
## Formula: ~x + y
## Parameter estimate(s):
## range nugget
## 402.2077831 0.2194023
##
## Coefficients:
## Value Std.Error t-value p-value
## (Intercept) 2.0306920 5.171732 0.3926522 0.6966
## Cordia.lasiocalyx 0.1508099 0.194940 0.7736210 0.4435
## Hirtella.triandra 0.0076692 0.091987 0.0833720 0.9340
## Picramnia.latifolia 0.2509289 0.539635 0.4649976 0.6443
## Quassia.amara 1.5049423 1.960799 0.7675147 0.4471
## Tabernaemontana.arborea 0.0322219 0.142012 0.2268964 0.8216
## Trattinnickia.aspera 1.7698936 0.583930 3.0310015 0.0042
## Xylopia.macrantha 0.4058061 0.161181 2.5177087 0.0157
##
## Correlation:
## (Intr) Crd.ls Hrtll. Pcrmn. Qss.mr Tbrnm. Trttn.
## Cordia.lasiocalyx -0.273
## Hirtella.triandra -0.272 -0.122
## Picramnia.latifolia 0.017 0.038 -0.387
## Quassia.amara -0.039 -0.304 0.337 -0.213
## Tabernaemontana.arborea -0.242 -0.029 0.166 -0.201 0.106
## Trattinnickia.aspera -0.090 0.163 -0.272 0.271 -0.646 -0.036
## Xylopia.macrantha -0.095 -0.055 -0.073 -0.035 0.295 0.143 -0.164
##
## Standardized residuals:
## Min Q1 Med Q3 Max
## -1.0645964 -0.5625847 -0.3564599 0.2563989 2.6599508
##
## Residual standard error: 7.348772
## Degrees of freedom: 50 total; 42 residualSpatial error terms did not effect the model
Adding spatial error terms (rational nugget) for the model with one species improved the model. Fitting error to the model that included all species improved the model, but adding nuggets had no effect. Overall, coefficients for both models had an impact, but this was larger for the model with only one species. Spatial error terms can control for spatial dependence between neighbors and therefore improve our model.